Comparing pluralities

What does it mean to compare sets of objects along a scale, for example by saying “the men are taller than the women”? We explore comparison of pluralities in two experiments, eliciting comparison judgments while varying the properties of the members of each set. We find that a plurality is judged as “bigger” when the mean size of its members is larger than the mean size of the competing plurality. These results are incompatible with previous accounts, in which plural comparison is inferred from many instances of singular comparison between the members of the sets (Matushansky &; Ruys, 2006). Our results suggest the need for a type of predication that ascribes properties to plural entities, not just individuals, based on aggregate statistics of their members. More generally, these results support the idea that sets and their properties are actively represented as single units.     

Comparing categorization models

Four experiments are presented that competitively test rule- and exemplar-based models of human categorization behavior. Participants classified stimuli that varied on a unidimensional axis into 2 categories. The stimuli did not consistently belong to a category; instead, they were probabilistically assigned. By manipulating these assignment probabilities, it was possible to produce stimuli for which exemplar- and rule-based explanations made qualitatively different predictions. F. G. Ashby and J. T. Townsend's (1986) rule-based general recognition theory provided a better account of the data than R. M. Nosofsky's (1986) exemplar-based generalized context model in conditions in which the to-be-classified stimuli were relatively confusable. However, generalized context model provided a better account when the stimuli were relatively few and distinct. These findings are consistent with multiple process accounts of categorization and demonstrate that stimulus confusion is a determining factor as 10 which process mediates categorization.     

Comparing dependent correlations

In a recent article in The Journal of General Psychology, J. B. Hittner, K. May, and N. C. Silver (2003) described their investigation of several methods for comparing dependent correlations and found that all can be unsatisfactory, in terms of Type I errors, even with a sample size of 300. More precisely, when researchers test at the .05 level, the actual Type I error probability can exceed .10. The authors of this article extended J. B. Hittner et al.'s research by considering a variety of alternative methods. They found 3 that avoid inflating the Type I error rate above the nominal level. However, a Monte Carlo simulation demonstrated that when the underlying distribution of scores violated the assumption of normality, 2 of these methods had relatively low power and had actual Type I error rates well below the nominal level. The authors report comparisons with E. J. Williams' (1959) method.     

Comparing latent distributions

We consider the problem of comparingm latent population distributions when the observed values are scores on a test battery with binary items. The latent densities are assumed to be normal densities, and we consider a test for equality of the means as well as a test equality of the variances. In addition, we consider a longitudinal model, where the test battery has been applied to the same individuals at different points in time. This model allows for correlations between the latent variable at different time points, and methods are discussed for estimating the correlation coefficient.This work was supported in part by a grant from the Danish Social Science Research Council.     

Comparing Computational Power

It is common practice to compare the computational power ofdifferent models of computation. For example, the recursivefunctions are strictly more powerful than the primitive recursivefunctions, because the latter are a proper subset of the former(which includes Ackermann's function). Side-by-side with this"containment" method of measuring power, it is also standardto base comparisons on "simulation". For example, one says thatthe (untyped) lambda calculus is as powerful—computationallyspeaking—as the partial recursive functions, because thelambda calculus can simulate all partial recursive functionsby encoding the natural numbers as Church numerals. The problem is that unbridled use of these two distinct waysof comparing power allows one to show that some computationalmodels (sets of partial functions) are strictly stronger thanthemselves! We argue that a better definition is that modelA is strictly stronger than B if A can simulate B via some encoding,whereas B cannot simulate A under any encoding. We show thatwith this definition, too, the recursive functions are strictlystronger than the primitive recursive. We also prove that therecursive functions, partial recursive functions, and Turingmachines are "complete", in the sense that no injective encodingcan make them equivalent to any "hypercomputational" model.¹     

Comparing Field Theories

While in broad agreement with many of the observations made by Donnel B. Stern, this essay emphasizes certain differences in how BFT in general and the work of Nino Ferro in particular are seen. These begin with the very meaning of the term, field, and include a less authoritarian view of the analyst's “knowing” the degree to which the analyst's unconscious and subjectivity are implicated in the creation of the field, and the nature and degree of the analyst's unconscious contribution to the creation of the field.     

Comparing item characteristic curves

Test items are often evaluated and compared by contrasting the shapes of their item characteristics curves (ICC's) or surfaces. The current paper develops and applies three general (i.e., nonparametric) comparisons of the shapes of two item characteristic surfaces: (i) proportional latent odds, (ii) uniform relative difficulty, and (iii) item sensitivity. Two items may be compared in these ways while making no assumption about the shapes of item characteristic surfaces for other items, and no assumption about the dimensionality of the latent variable. Also studied is a method for comparing the relative shapes of two item characteristic curves in two examinee populations.The author is grateful to Paul Holland, Robert Mislevy, Tue Tjur, Rebecca Zwick, the editor and reviewers for valuable comments on the subject of this paper, to Mari A. Pearlman for advice on the pairing of items in the examples, and to Dorothy Thayer for assistance with computing.     

Comparing dependent robust correlations

Let r₁ and r₂ be two dependent estimates of Pearson's correlation. There is a substantial literature on testing H₀ : ρ₁ = ρ₂, the hypothesis that the population correlation coefficients are equal. However, it is well known that Pearson's correlation is not robust. Even a single outlier can have a substantial impact on Pearson's correlation, resulting in a misleading understanding about the strength of the association among the bulk of the points. A way of mitigating this concern is to use a correlation coefficient that guards against outliers, many of which have been proposed. But apparently there are no results on how to compare dependent robust correlation coefficients when there is heteroscedasicity. Extant results suggest that a basic percentile bootstrap will perform reasonably well. This paper reports simulation results indicating the extent to which this is true when using Spearman's rho, a Winsorized correlation or a skipped correlation.     

Comparing solid-body with point-light animations

The movement of faces provides useful information for a variety of tasks and is now an active area of research. We compare here two ways of presenting face motion in experiments: as solid-body animations and as point-light displays. In the first experiment solid-body and point-light animations, based on the same motion-captured marker data, produced similar levels of performance on a sex-judgment task. The trend was for an advantage for the point-light displays, probably in part because of residual spatial cues available in such stimuli. In the second experiment we compared spatially normalised point-light displays of marker data with solid-body animations and pseudorandom point-light animations. Performance with solid-body animations and normalised point-light displays was similar and above chance, while performance with the pseudorandom point-light stimuli was not above chance. We conclude that both relatively few well-placed points and solid-body animations provide useful information about facial motion, but that a greater number of randomly placed points does not support above-chance performance. Solid-body animations have the methodological advantages of reducing the importance of marker placement and are more effective in isolating motion information, even if they are subsequently rendered as point-light displays.     

Comparing variances of correlated variables

A test is proposed for the equality of the variances ofk 2 correlated variables. Pitman's test fork = 2 reduces the null hypothesis to zero correlation between their sum and their difference. Its extension, eliminating nuisance parameters by a bootstrap procedure, is valid for any correlation structure between thek normally distributed variables. A Monte Carlo study for several combinations of sample sizes and number of variables is presented, comparing the level and power of the new method with previously published tests. Some nonnormal data are included, for which the empirical level tends to be slightly higher than the nominal one. The results show that our method is close in power to the asymptotic tests which are extremely sensitive to nonnormality, yet it is robust and much more powerful than other robust tests.This research was supported by the fund for the promotion of research at the Technion.     

Comparing examinees to a control

When comparing examinees to a control, the examiner usually does not know the probability of correctly classifying the examinees based on the number of items used and the number of examinees tested. Using ranking and selection techniques, a general framework is described for deriving a lower bound on this probability. We illustrate how these techniques can be applied to the binomial error model. New exact results are given for normal populations having unknown and unequal variances.The work upon which this publication is based was performed pursuant to a grant [Grant No. NIE-G-76-0083] with the National Institute of Education, Department of Health, Education and Welfare. Points of view or opinions stated do not necessarily represent official NIE position or policy.     

New Methods for Comparing Groups

Abstract— A commonly used method for comparing groups of individuals is the analysis of variance (ANOVA) F test. When the assumptions underlying the derivation of this test are true, its power, meaning its probability of detecting true differences among the groups, competes well with all other methods that might be used. But when these assumptions are false, its power can be relatively low. Many new statistical methods have been proposed—ones that are aimed at achieving about the same amount of power when the assumptions of the F test are true but which have the potential of high power in situations where the F test performs poorly. A brief summary of some relevant issues and recent developments is provided. Some related issues are discussed and implications for future research are described.     

Comparing excitatory backward and forward conditioning

Three Pavlovian lick suppression studies with rats were conducted to compare the role of the conditioning context in excitatory backward and forward conditioning. The experiments explored the possibility that excitatory backward conditioning, but not forward conditioning, is mediated by the context. That is, in excitatory backward conditioning, the conditioning context may function as an excitatory mediator, which supports second-order conditioning of the target cue. This possibility contrasts with traditional accounts, which suggests that common processes underlie excitatory backward and forward conditioning. Experiment 1 found that conditioned responding following backward conditioning was attenuated as a result of posttraining extinction of the training context, but the same manipulation elevated responding after forward conditioning. Experiments 2 and 3 found that posttraining and pretraining associative inflation of the context (presenting unsignalled USs) increased conditioned responding to the target of a backward conditioning procedure but either had no effect or reduced responding to the target of a forward conditioning procedure. Thus, excitatory backward and forward conditioning appear to differ in their dependence on the status of the conditioning context.     

四类不同心理契约关系的比较研究

根据企业对自己义务履行程度和员工对自己义务履行程度的不同,将员工的心理契约分成四种类型,两种情况。不同的情况下,员工的组织公民行为、离职倾向和对高层的信任存在显著差异。     

Comparing hierarchical models of personality pathology

Two dimensional, hierarchical classification models of personality pathology have emerged as alternatives to traditional categorical systems: multi-tiered models with increasing numbers of factors and models that distinguish between a general factor of severity and specific factors reflecting style. Using a large sample (N = 840) with a range of psychopathology, we conducted exploratory factor analyses of individual personality disorder criteria to evaluate the validity of these conceptual structures. We estimated an oblique, “unfolding” hierarchy and a bifactor model, then examined correlations between these and multi-method functioning measures to enrich interpretation. Four-factor solutions for each model, reflecting rotations of each other, fit well and equivalently. The resulting structures are consistent with previous empirical work and provide support for each theoretical model.     

Comparing factor structures of adolescent psychopathology

Research on the structure of adolescent psychopathology can provide information on broad factors that underlie different forms of maladjustment in youths. Multiple studies from the literature on adult populations suggest that 2 factors, Internalizing and Externalizing, meaningfully comprise the factor structure of adult psychopathology (e.g., Krueger, 1999) and presumably represent broad vulnerability for co-occurring disorders. Though this research was partially inspired by early work with children and adolescents (e.g., Achenbach & Edelbrock, 1984), the role of substance use in these models of youth psychopathology has not been fully explored. Toward this goal, we recruited 223 youths (10-17 years of age, M = 14.2) from mental health agencies and the community. We found evidence for a 3-factor model of youth psychopathology, including Internalizing (depression, generalized anxiety), Externalizing (conduct disorder, attention deficit, oppositional defiant disorder), and Substance Use (alcohol and cannabis). The 3-factor model showed the best fit to the data relative to other factor models tested, including across subsamples of adolescents who differed on level of psychopathology (treatment vs. community samples). Implications for the structure of adolescent psychopathology, including important developmental considerations, are discussed.